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Two lines concur on (ABC)

Source: XVII Sharygin Corespondnce Round P13

March 2, 2021

geometryexcircleincentermixtilinearconcurrencySharygin Geometry Olympiadanant mudgal geo

Problem Statement

In triangle

ABC

with circumcircle

\Omega

and incenter

I

, point

M

bisects arc

BAC

and line

\overline{AI}

meets

\Omega

at

N\ne A

. The excircle opposite to

A

touches

\overline{BC}

at point

E

. Point

Q\ne I

on the circumcircle of

\triangle MIN

is such that

\overline{QI}\parallel\overline{BC}

. Prove that the lines

\overline{AE}

and

\overline{QN}

meet on

\Omega

.

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